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> Well, it can’t use more than it can get from the sun that hits it. So it can’t need to radiate more than that away

You are correct that the first law of thermodynamics dictates the energy, but anyone who has parked a car in the sun will tell you, the temperature where the absorption/dissipation equilibrium is achieved is often incompatible with the survival of the cargo.

edit to your edit:

> Edit: ISS is about 90KW steady state, and the collector to radiator area ratio is about 5:1. Dunno about the mass ratio.

Cool; that's about half the wattage of one modern full-height Nvidia AI rack (172kW) - you need two ISSes to service just 1 rack; extrapolate that to a data center's worth of racks and see if the math is mathing. The ISS is about the size of a(n American) football field.

Again, just to remind you, I didn’t claim space datacenters are economically rational.
My original claim, in its entirety, was that on earth "You'll also get much better cooling for free via convection."
You sure will. My contribution is that you don’t need much better cooling.
The average temperature of a rock, car, or the ISS in low earth orbit is about -18C.
It's this huge misconception that space is super cold. A better mind model is that space doesn't have much of a temperature at all just cause there's nothing there. Vacuum doesn't have a temperature.

You won't immediately freeze if you enter space without a suit. You'll die almost immediately, but it will be because your blood will begin to boil because of the lack of pressure kinda like an extreme form of divers sickness - it's just not the cold that'll get you first.

That’s all true. But stuff in space has a temperature, and once I’d been dead a while in LEO, mine would be -18C.